The statement “a line can never intersect a plane at exactly two points” is either an axiom in some formalization of Euclidean geometry or follows so directly from one or two other axioms in the system that the answer seems empty of meaning, a restatement of definitions (as in some of the good answers here).
How do you know if a line intersects a plane?
Answer: a) To find the intersection we substitute the formulas for x, y and z into the equation for P and solve for t. The line is contained in the plane, i.e., all points of the line are in its intersection with the plane.
Do 2 points always create a line?
Collinear points are points that lie on a line. Any two points are always collinear because you can always connect them with a straight line. Three or more points can be collinear, but they don’t have to be. The above figure shows collinear points P, Q, and R which all lie on a single line.
Are two lines that don’t intersect parallel?
Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
How many lines can intersect on a plane?
Univ. The intersection of two planes is a line. If the planes do not intersect, they are parallel. They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat.
Does a line end?
A line has no end points. A line segment has two endpoints. A line segment connects both endpoints. If the two lines cannot meet at any point, they are called parallel lines.
What are two distinct lines?
They each write down what they think it means for two distinct lines in a plane to be parallel: Rachel writes, ”two distinct lines are parallel when they are both perpendicular to a third line.
Can 2 planes intersect at a segment?
They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat. One way to think about planes is to try to use sheets of paper, and observe that the intersection of two sheets would only happen at one line.
What happens at the intersection of a line and a plane?
If the line lies in the plane. In this case, the intersection is (obviously) a line. If the normal of the plane is not perpendicular to the line, they will intersect at exactly one point.
Can a line be a part of a plane?
a) The two intersect. So “nothing” is not a reasonable answer. b) If the line is a part of the plane, then it is a part of the plane and does not “intersect” but would be congruent with each other (LoL, congruency between different dimensions… Don’t think about it.
Why are all the points on a plane on the line?
If you pick two points on a plane and connect them with a straight line then every point on the line will be on the plane. Given two points there is only one line passing those points. Thus if two points of a line intersect a plane then all points of the line are on the plane. share|cite|improve this answer.
Can a line pass through a plane more than once?
The difficulty in proving this comes from the fact that whether or not a line, not on a plane, can intersect the plane in more than one place is equivalent to Euclid’s 5th postulate. So in geometries where two parallel lines may intersect more than once, a line may also pass through a plane more than once.
